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Dispersion curves to a oscillatory reaction-diffusion system with the self-consistent flow have obtained by means of numerical calculations. The flow modulates the shape of dispersion curves and characteristics of traveling waves. The point…
We develop a numerical methodology for the computation of entanglement measures for mixed quantum states. Using the well-known Schr\"odinger-HJW theorem, the computation of convex roof entanglement measures is reframed as a search for…
In arXiv:2305.03945 [math.NA], a first-order optimization algorithm has been introduced to solve time-implicit schemes of reaction-diffusion equations. In this research, we conduct theoretical studies on this first-order algorithm equipped…
In this paper, we propose a lattice Boltzmann (LB) model for the generalized coupled cross-diffusion-fluid system. Through the direct Taylor expansion method, the proposed LB model can correctly recover the macroscopic equations. The cross…
A method of numerically evaluating slowly convergent monotone series is described. First, we apply a condensation transformation due to Van Wijngaarden to the original series. This transforms the original monotone series into an alternating…
The convergence problem for scattering states is studied in detail within the framework of the Algebraic Model, a representation of the Schrodinger equation in an L^2 basis. The dynamical equations of this model are reformulated featuring…
The advantage of particle Lagrangian methods in computational fluid dynamics is that advection is accurately modeled. However, this complicates the calculation of space derivatives. If a mesh is employed, it must be updated at each time…
This work focuses on numerically solving a shape identification problem related to advection-diffusion processes with space-dependent coefficients using shape optimization techniques. Two boundary-type cost functionals are considered, and…
Schwarz methods are attractive parallel solvers for large scale linear systems obtained when partial differential equations are discretized. For hybridizable discontinuous Galerkin (HDG) methods, this is a relatively new field of research,…
We consider nonlinear partial differential equations (PDEs) for advection-diffusion processes which are augmented by an auxiliary parameter $\delta$ such that $\delta=0$ corresponds to linear advection-diffusion. We derive potentially…
A solution is developed for a convection-diffusion equation describing chemical transport with sorption, decay, and production. The problem is formulated in a finite domain where the appropriate conservation law yields Robin conditions at…
A space discrete approximation to a highly nonlinear reaction-diffusion system endowed with a stochastic dynamical boundary condition is analyzed and the convergence of the discrete scheme to the solution to the corresponding continuum…
High-velocity fluid flow through porous media is modeled by prescribing a nonlinear relationship between the flow rate and the pressure gradient, called the Darcy--Forchheimer equation. This paper is concerned with the analysis of parallel…
In this paper we propose and analyse a new formulation and pointwise divergence-free mixed finite element methods for the numerical approximation of Darcy--Brinkman equations in vorticity--velocity--pressure form, coupled with a transport…
The focus of this paper is on the concurrent reconstruction of both the diffusion and potential coefficients present in an elliptic/parabolic equation, utilizing two internal measurements of the solutions. A decoupled algorithm is…
We explore the framework of a real-time coupled cluster method with a focus on improving its computational efficiency. Propagation of the wave function via the time-dependent Schr\"odinger equation places high demands on computing…
In this work we derive a posteriori error estimates for the convection-diffusion-reaction equation coupled with the Darcy-Forchheimer problem by a nonlinear external source depending on the concentration of the fluid. We introduce the…
Due to extreme difficulties in numerical simulations of Euler-Maxwell equations, which are caused by the highly complicated structures of the equations, this paper concerns the simplification of Euler-Maxwell system through the…
The Peaceman--Rachford scheme is a commonly used splitting method for discretizing semilinear evolution equations, where the vector fields are given by the sum of one linear and one nonlinear dissipative operator. Typical examples of such…
We present a numerical approximation method for linear diffusion-reaction problems with possibly discontinuous Dirichlet boundary conditions. The solution of such problems can be represented as a linear combination of explicitly known…